56
ɩɥɢɬɵ ɫɱɢɬɚɸɬɫɹ ɩɨɥɨɠɢɬɟɥɶɧɵɦɢ
Ɉɞɧɚɤɨ ɢɡ ɚɧɚɥɢɡɚ ɮɨɪɦɭɥ ɫ ɩɪɢɜɟɞɟɧɧɵɦɢ ɧɨɦɟɪɚɦɢ ɜɢɞɧɨ, ɱɬɨ ɫɦɟɧɚ ɧɚɩɪɚɜɥɟɧɢɹ
ɤɨɨɪɞɢɧɚɬɧɨɣ ɨɫɢ Z ɢɡɦɟɧɹɟɬ ɡɧɚɤ ɜɬɨɪɵɯ ɩɪɨɢɡɜɨɞɧɵɯ ɜ ɭɤɚɡɚɧɧɵɯ ɮɨɪɦɭɥɚɯ .
ɉɨɷɬɨɦɭ ɩɨɥɭɱɟɧɧɵɟ ɮɨɪɦɭɥɵ ɫɩɪɚɜɟɞɥɢɜɵ ɬɨɥɶɤɨ ɞɥɹ ɜɚɪɢɚɧɬɚ, ɤɨɝɞɚ ɨɫɶ Z
ɧɚɩɪɚɜɥɟɧɚ ɜɧɢɡ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɞɥɹ ɪɚɫɫɦɨɬɪɟɧɧɨɣ ɧɚ ɪɢɫ. 4.7 ɢ ɪɢɫ 4.6 ɞɟɮɨɪɦɚɰɢɢ ɩɥɢɬɵ
ɜɬɨɪɵɟ ɩɪɨɢɡɜɨɞɧɵɟ ɹɜɥɹɸɬɫɹ ɨɬɪɢɰɚɬɟɥɶɧɵɦɢ. ɉɨɷɬɨɦɭ ɜɵɱɢɫɥɟɧɧɵɟ ɩɨ ɭɤɚɡɚɧɧɵɦ
ɮɨɪɦɭɥɚɦ
ɦɨɦɟɧɬɵ ɩɨɥɭɱɚɬɫɹ ɩɨɥɨɠɢɬɟɥɶɧɵɦɢ ɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦɢ ɩɨ ɩɪɚɜɢɥɭ ɡɧɚɤɨɜ
ɧɨɪɦɚɥɶɧɵɦ ɧɚɩɪɹɠɟɧɢɹɦ.
ɉɪɢ ɧɚɩɪɚɜɥɟɧɢɢ ɨɫɢ Z ɜɜɟɪɯ ɜ ɮɨɪɦɭɥɚɯ (4.14), (4.16) ɢ (4,20) ɫɥɟɞɭɟɬ ɩɪɢɧɹɬɶ ɡɧɚɤ
«ɩɥɸɫ», ɩɨɫɤɨɥɶɤɭ ɜɬɨɪɵɟ ɩɪɨɢɡɜɨɞɧɵɟ ɞɥɹ ɷɬɨɝɨ ɜɚɪɢɚɧɬɚ ɧɚɩɪɚɜɥɟɧɢɹ ɤɨɨɪɞɢɧɚɬɧɨɣ ɨɫɢ
ɫɬɚɧɭɬ ɩɨɥɨɠɢɬɟɥɶɧɵɦɢ.
ɉɪɢɦɟɱɚɧɢɟ ɤ ɜɨɩɪɨɫɭ ɨ ɡɧɚɤɚɯ ɜ ɮɨɪɦɭɥɚɯ (4.17), (4.21) ɩɪɢ ɜɵɱɢɫɥɟɧɢɢ
ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɧɚɩɪɹɠɟɧɢɣ
yx
VV
, ɢ ɤɚɫɚɬɟɥɶɧɵɯ ɧɚɩɪɹɠɟɧɢɣ
xy
ȼ ɮɨɪɦɭɥɚɯ (4.17) ɢ (4.18) ɩɪɟɞɩɨɥɚɝɚɟɬɫɹ, ɱɬɨ ɢɡɝɢɛɚɸɳɢɟ ɦɨɦɟɧɬɵ
yx
MM , ɩɨɥɨɠɢɬɟɥɶɧɵ, ɤɨɝɞɚ ɨɧɢ ɪɚɫɬɹɝɢɜɚɸɬ ɧɢɠɧɸɸ ɫɬɨɪɨɧɭ ɩɥɢɬɵ. ɉɪɢ
ɜɵɩɭɤɥɨɫɬɢ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɩɥɢɬɵ ɧɚɩɪɚɜɥɟɧɧɨɣ ɜɧɢɡ ɷɬɢ ɦɨɦɟɧɬɵ ɬɚɤɨɜɵɦɢ ɢ ɹɜɥɹɸɬɫɹ
(ɫɦ. ɪɢɫ.4.7).
ɉɨɫɤɨɥɶɤɭ ɨɫɶ Z ɜ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɦ ɜɚɪɢɚɧɬɟ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɵ ɩɥɢɬɵ ɧɚɩɪɚɜɥɟɧɚ
ɜɧɢɡ (ɫɦ. ɪɢɫ.4.4,ɚ), ɬɨ ɞɥɹ ɬɨɱɟɤ ɩɥɢɬɵ, ɪɚɫɩɨɥɨɠɟɧɧɵɯ ɧɢɠɟ ɟɟ ɫɪɟɞɢɧɧɨɣ ɩɥɨɫɤɨɫɬɢ, ɜ
ɮɨɪɦɭɥɵ (4.17) ɩɨɞɫɬɚɜɥɹɟɦ
0!z . Ɍɨɝɞɚ, ɩɪɢ ɩɨɥɨɠɢɬɟɥɶɧɵɯ ɢɡɝɢɛɚɸɳɢɯ ɦɨɦɟɧɬɚɯ,
ɩɨɥɭɱɚɟɦ ɜ ɡɨɧɟ ɩɥɢɬɵ ɧɢɠɟ ɫɪɟɞɢɧɧɨɣ ɩɥɨɫɤɨɫɬɢ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɩɨɥɨɠɢɬɟɥɶɧɵɟ ɩɨ ɡɧɚɤɭ
(ɪɚɫɬɹɝɢɜɚɸɳɢɟ) ɧɨɪɦɚɥɶɧɵɟ ɧɚɩɪɹɠɟɧɢɹ.
ȿɫɥɢ ɜ ɤɨɨɪɞɢɧɚɬɧɨɣ ɫɢɫɬɟɦɟ, ɤ ɤɨɬɨɪɨɣ ɨɬɧɟɫɟɧɚ ɩɥɢɬɚ, ɨɫɶ Z ɧɚɩɪɚɜɥɟɧɚ ɜɜɟɪɯ, ɬɨ
ɨɬ ɷɬɨɝɨ ɧɚɩɪɹɠɟɧɧɨɟ ɫɨɫɬɨɹɧɢɟ ɩɥɢɬɵ ɧɟ ɢɡɦɟɧɢɬɫɹ. ɉɨ-ɩɪɟɠɧɟɦɭ ɪɚɫɬɹɧɭɬɵɦɢ ɛɭɞɭɬ
ɧɢɠɧɢɟ «ɜɨɥɨɤɧɚ» ɩɥɢɬɵ. ɂ ɢɡɝɢɛɚɸɳɢɟ ɦɨɦɟɧɬɵ, ɪɚɫɬɹɝɢɜɚɸɳɢɟ ɧɢɠɧɢɟ ɜɨɥɨɤɧɚ, ɩɨ-
ɩɪɟɠɧɟɦɭ ɫɱɢɬɚɸɬɫɹ ɩɨɥɨɠɢɬɟɥɶɧɵɦɢ.
ɇɨ ɬɟɩɟɪɶ ɜ ɮɨɪɦɭɥɵ (4.17) ɞɥɹ ɬɨɱɟɤ ɩɥɢɬɵ ɧɢɠɟ ɫɪɟɞɢɧɧɨɣ ɩɥɨɫɤɨɫɬɢ ɧɟɨɛɯɨɞɢɦɨ
ɩɨɞɫɬɚɜɥɹɬɶ
0z . ɗɬɨ ɩɪɢɜɟɞɟɬ ɤ ɬɨɦɭ, ɱɬɨ ɩɪɢ ɜɵɱɢɫɥɟɧɢɢ ɹɜɧɨ ɪɚɫɬɹɝɢɜɚɸɳɢɯ
ɧɨɪɦɚɥɶɧɵɯ ɧɚɩɪɹɠɟɧɢɣ ɩɨɥɭɱɢɦ ɢɯ ɫɨ ɡɧɚɤɨɦ «ɦɢɧɭɫ». ɑɬɨɛɵ ɩɨɥɭɱɢɬɶ ɡɧɚɤ ɩɥɸɫ,
ɧɟɨɛɯɨɞɢɦɨ ɞɥɹ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɵ ɩɥɢɬɵ
ɫɨɫɶɸ Z, ɧɚɩɪɚɜɥɟɧɧɨɣ ɜɜɟɪɯ, ɜ ɮɨɪɦɭɥɚɯ (4.17)
ɩɨɫɬɚɜɢɬɶ ɡɧɚɤ «ɦɢɧɭɫ»:
z
M
z
M
y
y
x
x
VV
;.
(4.17*)
Ⱥɧɚɥɨɝɢɱɧɨ ɞɥɹ ɤɚɫɚɬɟɥɶɧɵɯ ɧɚɩɪɹɠɟɧɢɣ ɜ ɮɨɪɦɭɥɟ (4.21) ɬɚɤɠɟ ɧɟɨɛɯɨɞɢɦɨ
ɩɨɫɬɚɜɢɬɶ ɡɧɚɤ «ɦɢɧɭɫ»:
z
M
xy
xy
W
.
(4.21 *)
Ɉɫɬɚɥɨɫɶ ɨɩɪɟɞɟɥɢɬɶ ɧɚ ɪɚɫɫɦɚɬɪɢɜɚɟɦɵɯ ɫɟɱɟɧɢɹɯ ɤɚɫɚɬɟɥɶɧɵɟ
ɧɚɩɪɹɠɟɧɢɹ
xz
W
ɢ
yz
. Ɉɧɢ ɞɟɣɫɬɜɭɸɬ ɧɚ ɩɥɨɳɚɞɤɚɯ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɵɯ
ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɨɫɹɦ X ɢ Y ɜ ɧɚɩɪɚɜɥɟɧɢɢ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɦ ɫɪɟɞɢɧɧɨɣ